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Quadratic Functions Graphs
In Standard Form
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Graphing Quadratic Functions
Quadratic functions have the form: y = ax2 + bx + c When we graph them, they make a parabola!
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Vertex of a Parabola A parabola can open up or down.
y x The vertex of a parabola is the highest or lowest point of the parabola. Vertex
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y = ax2 + bx + c The standard form of a quadratic function is:
The parabola will open up when the a is positive. a < 0 a > 0 The parabola will open down when the a is negative.
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The line of symmetry ALWAYS passes through the vertex.
If we drew a line down the middle of the parabola, we call this line the line of symmetry. y x The line of symmetry ALWAYS passes through the vertex.
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How do we find the Line of Symmetry?
Given that a function is in the form: For example, find the line of symmetry of y = 3x2 – 18x + 7 y = ax2 + bx + c The equation of the line of symmetry is
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How do we find the vertex?
We know that the vertex is a coordinate (x, y). If we know the line of symmetry, we know the x coordinate! Now we, just plug x into to find the y coordinate. y = 3x2 – 18x + 7 STEP 1: Find the line of symmetry. y = ax2 + bx + c STEP 2: Plug the x – value into the original equation to find the y value.
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A Quadratic Function in Standard Form
There are 5 steps to graphing a parabola in standard form. STEP 1: Find the axis of symmetry using STEP 2: Find the vertex: ( , plug in ) STEP 3: Find the y-intercept (value of c) STEP 4: Plot the matching or symmetrical point STEP 5: Sketch your curve
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A Quadratic Function in Standard Form
y = 2x2 – 4x – 1 y x STEP 1: AOS STEP 2: vertex STEP 3: y-intercept STEP 4: symmetrical point STEP 5: graph parabola
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You try! y = -2x2 – 4x + 3 y x
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